Research Article
Model-based calculating tool for pollen-mediated gene
flow frequencies in plants
Lei Wang and Bao-Rong Lu*
Ministry of Education Key Laboratory for Biodiversity and Ecological Engineering, Department of Ecology and Evolutionary Biology,
Fudan University, Songhu Road 2005, Shanghai 200438, China
Received: 13 July 2016; Editorial decision: 29 November 2016; Accepted: 6 December 2016; Published: 30 December 2016
Associate Editor: Diana Wolf
Citation: Wang L, Lu B-R. 2017. Model-based calculating tool for pollen-mediated gene flow frequencies in plants. AoB PLANTS 9:
plw086; doi:10.1093/aobpla/plw086
Abstract. The potential social-economic and environmental impacts caused by transgene flow from genetically
engineered (GE) crops have stimulated worldwide biosafety concerns. To determine transgene flow frequencies resulted from pollination is the first critical step for assessing such impacts, in addition to the determination of transgene expression and fitness in crop-wild hybrid descendants. Two methods are commonly used to estimate pollenmediated gene flow (PMGF) frequencies: field experimenting and mathematical modelling. Field experiments can
provide relatively accurate results but are time/resource consuming. Modelling offers an effective complement for
PMGF experimental assessment. However, many published models describe PMGF by mathematical equations and
are practically not easy to use. To increase the application of PMGF modelling for the estimation of transgene flow,
we established a tool to calculate PMGF frequencies based on a quasi-mechanistic PMGF model for wind-pollination
species. This tool includes a calculating program displayed by an easy-operating interface. Pollen-mediated gene
flow frequencies of different plant species can be quickly calculated under different environmental conditions by
including a number of biological and wind speed parameters that can be measured in the fields/laboratories or obtained from published data. The tool is freely available in the public domain (http://ecology.fudan.edu.cn/userfiles/
cn/files/Tool_Manual.zip (14 December 2016)). Case studies including rice, wheat and maize demonstrated similar
results between the calculated frequencies based on this tool and those from published PMGF data. This PMGF calculating tool will provide useful information for assessing and monitoring social-economic and environmental impacts
caused by transgene flow from GE crops. This tool can also be applied to determine the isolation distances between
GE and non-GE crops in a coexistence agro-ecosystem, and to ensure the purity of certified seeds by setting proper
isolation distances among field production plots.
Keywords:
Biosafety assessment; coexistence; isolation distance; modelling; pollen-mediated gene flow; seed
production.
Introduction
The extensive cultivation of genetically engineered (GE)
crops has stimulated worldwide concerns over biosafety
issues (Timmons et al. 1996; Mehrotra and Goyal 2013).
The undesired social-economic and environmental impacts caused by transgene flow from a GE crop to its
* Corresponding author’s e-mail address: [email protected]
C The Authors 2016. Published by Oxford University Press on behalf of the Annals of Botany Company.
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/
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non-GE varieties (crop-to-crop) and wild relatives (cropto-wild/weed) are among the most concerned and
debated issues (Ellstrand et al. 1999; Stewart et al. 2003;
Andow and Zwahlen 2006; Lu 2016). Crop-to-crop transgene flow may cause adventitious presence (contamination) of transgenes in the non-GE crop varieties. Such
transgenic ‘contamination’ of non-GE crop varieties may
create regional or/and international trade problems or
even legal disputes (Metz and Fütterer 2002). Crop-towild/weed transgene flow may result in unwanted environmental impacts (Ellstrand 2003; Lu and Snow 2005; Lu
and Yang 2009; Ellstrand et al. 2013). It is essential to assess such impacts before commercial cultivation of GE
crops. The assessment of transgene flow and its potential impacts includes the estimation of (trans)gene flow
frequencies, transgene expression in crop-wild/weed hybrid descendants, and fitness effects caused by transgenes (Stewart et al. 2003; Snow et al. 2008; Lu and Yang
2009; Lu et al. 2016). If the frequency of transgene flow
is moderate to high, the expected environmental consequences and impacts might be substantial (Yong and
Kim 2001; Rong et al. 2005), and vice versa. Therefore,
the determination of (trans)gene flow frequencies is the
first key step to assess the potential social-economic and
environmental impacts caused by transgene introgression into wild/weedy relative species (Ellstrand 1992,
2003; Yong and Kim 2001; Lu and Snow 2005; Loureiro
et al. 2009; Lu and Yang 2009; Ellstrand et al. 2013).
Two methods are commonly used to measure the frequencies of pollen-mediated gene flow (PMGF): field experimenting and mathematical modelling. To date, field
experimenting is the major method to determine cropto-crop and crop-to-wild/weed PMGF frequencies at various spatial distance intervals (Song et al. 2003a; Chen
et al. 2004; Rong et al. 2004, 2005, 2007; Beckie et al.
2008). However, generating PMGF data from field experiments are usually time and resource consuming, although reliable PMGF frequencies can be obtained under
specific environmental conditions. In addition, PMGF frequencies estimated from a limited number of field experiments may not represent PMGF frequencies of a
particular plant species under diverse environmental
conditions. As a comparison, mathematical modelling
can provide relatively quick estimation of PMGF frequencies for different plant species under diverse environmental conditions (Yao et al. 2008; Rong et al. 2010; Hu
et al. 2014). Undoubtedly, mathematical modelling provides a powerful complement of the field-experimentbased method to estimate PMGF frequencies, provided
that the model can accurately simulate PMGF (Rong
et al. 2010; Wang et al. 2016).
Many PMGF models have been established (Loos et al.
2003; Klein et al. 2006; Yao et al. 2008; Wang and Yang
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2010; Hu et al. 2014). However, some of these models essentially simulate the variation patterns/dynamics of
PMGF or describe parameters that affect PMGF frequencies (Loos et al. 2003; Klein et al. 2006). In addition, other
PMGF models are also used to assess the maximum
PMGF frequencies at a particular spatial distance interval
(Gustafson et al. 2005; Gaines et al. 2007). Such features
make these models difficult to be applied directly to predict PMGF frequencies under specific situations.
Furthermore, many PMGF models only include sophisticated equations or functions (Yao et al. 2008; Wang and
Yang 2010; Hu et al. 2014), which puzzles the users who
are not familiar with the theories and skills of modelling.
It is difficult for the users to directly use these models to
estimate PMGF frequencies. For example, some PMGF
models only included mathematical equations that were
generated from two-dimensional Gaussian distribution
and double integral to describe PMGF patterns (Yao et al.
2008; Hu et al. 2014), challenging for common users. The
above limitation hinders the application of mathematical
modelling for the prediction of PMGF frequencies. Thus,
to establish a practical and easy-operating tool that can
be used to accurately calculate PMGF frequencies based
on an appropriate model will be useful for biologists,
managers and regulators. Such a tool will facilitate the
assessment and monitoring of transgene flow and its
social-economic and environmental impacts (Lu and
Snow 2005; Lu and Yang 2009; Lu 2016).
A number of factors should be considered when transforming a theoretical PMGF model into a practical and
easy-operating tool to calculate PMGF frequencies. First,
an appropriate PMGF model that can accurately estimate
PMGF frequencies should be selected for the tool construction. Second, the key parameters used for calculating PMGF frequencies should be easily measured from
the target plant species and environment at the site (in
situ) where the estimation of PMGF frequencies are
required, without conducting additional PMGF experiments. Third, a simple and easy human–computer communication/interaction interface that is accessible
through the Internet worldwide should be established
and ready to use. Therefore, anyone from any part of the
world can use this tool to calculate PMGF frequencies
under diverse environmental conditions, provided that
the required parameters are measured based on field- or
laboratory-experiments, in addition to published data.
The objective of this study is to establish a practical
tool or programme for the calculation of gene flow frequencies based on an existing PMGF model. To meet
such an objective, we need to (i) select an appropriate
PMGF model for constructing the tool; (ii) determine
suitable and easy-measurable parameters for the
PMGF tool calculation and (iii) construct a simple and
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easy-operating interface for the human–computer dialogs. In addition, the predicting power of this PMGF calculating tool should be tested by comparing the PMGF
frequencies obtained from the tool and field experiments. The establishment of this PMGF calculating tool
can substantially facilitate biosafety assessment of
transgene flow by efficiently and accurately calculating
PMGF frequencies under different environmental conditions, in addition to designing spatial isolation distances
between GE and non-GE crops in the coexistence farming
system, and for certified seed production.
Methods
Determination of model and parameters
To calculate gene flow frequencies accurately, without
conducting field experiments, we should select a suitable
PMGF model with the following features for the tool construction: (i) the model should include biological and climatic parameters that can essentially determine the
PMGF frequencies; (ii) generating data or parameters
from PMGF experiments is not required during model
simulation; (iii) the obtained PMGF frequencies from
model simulation should be highly consistent with the
field-experimental generated PMGF frequencies.
Similarly, the parameters used for the calculation of
PMGF frequencies should meet the following criteria:
(i) easily measureable from the environment in situ or
obtained from published data; (ii) sensitive to determine
the change of PMGF frequencies. In addition, the knowledge of interrelationships between PMGF and the parameters should be clearly understood or determined in
the previously published studies.
the three crop species. These data were used to examine
the predicting power of the PMGF calculating tool by
comparing the results generated by the model simulation and those obtained from the PMGF experiments. In
addition, all the biological parameters required by the
calculating tool are accessible for the three crop species.
For the required parameters, pollen diameter (the
diameter of pollen grains) of the three species was determined based on data from published studies (Goss 1968;
Chaturvedi et al. 1998). The parameter of relative pollen
release height was determined following the method
described in Wang et al. (2016). The parameter of outcrossing rate was estimated based on the natural hybridization rate (the proportion of hybrid seeds in total seed
set) measured at the nearest distances for rice
(Messeguer et al. 2001; Rong et al. 2005), wheat (Griffin
1987; Martin 1990) and maize (Goggi et al. 2007; Porta
et al. 2008). The parameter of crossability was determined as an average of 90 % for crop-to-crop gene flow.
The parameter of wind speed was determined following
the actual wind speed measured in the PMGF experiments of case studies.
Results
Model and parameters
Following the above criteria, we selected the quasimechanistic model described by Wang et al. (2016) to
construct the PMGF calculating tool. This model included
an inverse Gaussian function to describe the pollen dispersal pattern of wind-pollinated plants. The model is
shown as follows:
dAB DA
dAB DA þ DB
dAB ðuðx þ bÞ uðxÞÞ
¼ tB
dAB ðuðx þ bÞ uðxÞÞ þ uðx RÞ
FAB ðxÞ ¼ tB
Construction of the calculating tool
To create a human–computer dialog system with an
easy-operating and visualized interface, we decided to
construct the calculating tool (programme) for PMGF frequencies using the Visual Basic (VB) language (Microsoft
Corporation). Numerical integrations for PMGF calculation followed the Simpson integration method (Davis
and Rabinowitz 1979). The outputs of calculated PMGF
frequencies were described either as a value (frequency)
at a given spatial distance interval, or as a curve (frequencies) at a series of spatial distance intervals in plotting field after all the required parameters were
included.
Case studies: calculating PMGF frequencies
Three wind-pollination crop species were selected for
case studies: rice, wheat and maize. This is because published data from the PMGF experiments are available for
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(1)
where the u is the cumulative distribution function of the
inverse Gaussian function (Katul et al. 2005) and can be
calculated based on three parameters: pollen diameter,
pollen release height and wind speed [see equations (2–4)
in Wang et al. 2016]; tB indicates the outcrossing rate of a
recipient; dAB indicates the crossability between a pollen
donor and recipient; x indicates the variable of distance to
recipient; b indicates the depth of a donor field (determined as infinite for the worst scenario assessment in the
calculating tool). Through the replacement of the exponential function in the model of Rong et al. (2010) by the
function u, the model of Wang et al. (2016) can easily use
the measurable parameters to estimate PMGF frequencies. In addition, this model contained both biological and
climatic parameters that can be measured at the field
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sites where PMGF frequencies are attempted for PMGF calculation, which can provide more accurate results.
Furthermore, this model can provide highly consistent
PMGF frequencies with those generated from PMGF experiments. Therefore, this model is suitable for constructing the PMGF calculating tool. Detailed information of this
PMGF model is described in the published article (open access) by Wang et al. (2016) that is available at the link:
(http://journals.plos.org/plosone/article/asset?id¼10.1371
%2Fjournal.pone.0149563.PDF (14 December 2016)).
Apparently, the calculating tool can be used to generate
PMGF frequencies through model simulation, independent
of a particular PMGF experiment.
For the criteria of easy measurement, five parameters
were identified for constructing the PMGF calculating
tool. These included the diameter of donor’s pollen, pollen release height, outcrossing rate of pollen recipients,
crossability between pollen donors and recipients, and
wind speed. Detail description of the five parameters and
methods of their measurement are indicated as follows.
Pollen diameter (lm). The average diameter of pollen
grains from a pollen donor, which can be obtained by directly measuring diameters of 20–30 pollen grains under
a microscope.
Pollen release height (m). The average vertical differences between the height of updraft pollen (male flowers) from donor plants and flowers of recipient plants
(for detail see Fig. 1 in Wang et al. 2016). The average
height of the updraft pollen can be measured using the
pollen trap method (Song et al. 2004). Pollen release
height can be obtained by measuring the average height
of updraft pollen grains and flowers from about 10
plants.
Outcrossing rate (%). The probability of mating in
plants in which a male gamete in one individual (any
plant) fertilizes a female gamete in another individual
(recipient) (Waines and Hegde 2003), which can be estimated by hybridization experiments or using molecular
markers (Ritland et al. 1981; Xia et al. 2011).
Crossability (%). The ability of two individuals (a donor
and a recipient) to cross or hybridize (Schlegel 2003),
which can be estimated by measuring the ratio of hybrid
seeds generated from artificial crosses between donor
and recipient plant species/taxa.
Wind speed (m/s). The average horizontal wind speed
at the canopy height of donors and recipients, which can
be measured using an anemometer at the sites where
PMGF frequencies will be estimated.
In addition, the PMGF calculating tool also included
two variables: (i) Distance to recipient (m) that is defined
as the distances from the edge of a donor field to target
recipient plants; (ii) Threshold frequency (%) that is designed to calculate the spatial isolation distance (m) to
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Figure 1. Interface of the calculating tool for PMGF. (A) The initial
interface when tool is run; (B) the pop-up window defining the parameter of ‘Pollen diameter’ when clicking the ‘Pollen diameter’ input text; (C) the pop-up window reminding users when improper
values are included.
guarantee the GE crop contamination under the permitted low-level presence (LLP). The distance to recipients
can be determined as the initial distance where the
PMGF frequency needs for calculation from the edge of a
donor field to recipient plants. The threshold frequency
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can be determined according to the users’ requirement
in different countries or regions. With the five parameters
and two variables, the tool can be used to calculate
PMGF frequencies for different pairs (donors and recipients) of plant species and a spatial isolation distance (m)
required by meeting a particular threshold frequency (%)
under various environmental conditions.
Interface of the calculating tool
The established PMGF calculating tool and a user’s manual can be downloaded from the web site by clicking the
link at: http://ecology.fudan.edu.cn/userfiles/cn/files/
Tool_Manual.zip (14 December 2016). After clicking, a
pop-up window with a download file ‘Tool_Manual.zip’ or
download prompt requesting the path to save the zip file
will appear. Download the ‘Tool_Manual.zip’ file to a
computer and unzip it. An executable file named
‘Calculating tool for pollen-mediated gene flow.exe’
(152 kb) and a PDF file named ‘User’s Manual_
Calculating Tool for Gene Flow Frequencies’ will be available in the folder. The manual will provide a step-wise
guide for users to calculate PMGF frequencies. The executable file for the tool can be directly run by double
clicking. After that, an initial interface with all required input textboxes (parameter/variable), output texts including PMGF frequency (F) and distance for threshold (D), a
plotting field and commanding buttons (Fig. 1A) will be
displayed. Information or explanation about the parameters and variables included in the tool will be displayed
in a pop-up window when clicking the relevant input
texts (e.g. pollen diameter) at the left side of the interface (Fig. 1B).
Once all the required data for the five parameters and
the ‘distance to recipient’ variable are included in the
relevant textboxes, the expected PMGF frequencies of
the target plant species can be calculated and displayed
by clicking the ‘Gene flow frequency (F)’ and ‘Frequency
decline by distance’ buttons. Pollen-mediated gene flow
frequency (lower side of the interface) at a given spatial
distance interval can be calculated by clicking the ‘Gene
flow frequency (F)’ button. A series of PMGF frequencies
(right side of the interface) at a certain distance range
can be plotted as a curve by clicking the ‘Frequency decline by distance’ button. Gridlines can be added in the
plotting field to estimate PMGF frequencies at particular
distance intervals by clicking the ‘Gridlines’ button.
In addition, if non-numerical or improper values (e.g.
pollen diameter as 1000 lm) are included in the textboxes, this tool will display a pop-up window to warn the
users ‘Please input a PROPER value’ (Fig. 1C).
Pollen-mediated gene flow frequencies at various distances along the frequency curve (red) will be displayed in
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Figure 2. Different functions of the calculating tool for PMGF. (A)
the display of a particular frequency (0.08 %) at a distance interval
(10.2 m) in a floating window at the mouse cursor on the PMGF frequency curve; (B) the content of an output file showing the exported values of series PMGF frequencies (%) at every 1 m distance
intervals (m); (C) the value of isolation distance (7.8 m) determined
by the threshold PMGF frequency (0.1 %).
a floating window when moving the mouse cursor on the
curve shown in the plotting field after clicking the
‘Frequency decline by distance’ button (Fig. 2A). An output
file (PMGF frequencies at 1 m distance intervals.txt) with
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PMGF frequency (%) and distance (m) along the curve at
the distance intervals of 1 m will be generated and exported to the folder containing the calculating tool, by
clicking the ‘Output’ button (at the lower-right corner)
(Fig. 2B). In addition, the spatial isolation distance for a
particular threshold PMGF frequency can be calculated
and displayed when clicking the ‘Distance for threshold
(D)’ button (at the lower-left corner) after all the required
parameters and a particular ‘Threshold frequency’ (variable) are included (Fig. 2C, at the lower side).
Case studies: crop-to-crop gene flow
PMGE frequencies of rice. Using rice crop-to-crop gene
flow as an example, we estimated PMGF frequencies of
this crop by including five parameters obtained from
published results: pollen diameter to be 40 lm, pollen release height to be 0.5 m, outcrossing rate to be 1 %,
crossability as 90 % and wind speed to be 1 m s1 (Bae
et al. 2013; Wang et al. 2016).
After the inclusion of the five parameters (Fig. 3A) and
distance to recipient (e.g. 0.3 m) in the respective textboxes, and clicking the ‘Gene flow frequency (F)’ button,
a calculated PMGF frequency (F ¼ 0.46 %) for the target
rice recipient at a given spatial distance interval (0.3 m)
was displayed in the window (Fig. 3A, at the lower side).
When clicking the ‘Frequency decline by distance’ button, a series of calculated PMGF frequencies (0.46–
0.0028 %, as a curve) for a given spatial-distance range
(0.3–80 m) was displayed in the plotting field (Fig. 3B, at
the right). When clicking the ‘Gridlines’ button, gridlines
for different distance intervals (m) and PMGF frequencies
(%) were provided in the plotting field (Fig. 3C). Because
this tool is based on the deterministic model and include
determined parameters for PMGF calculation, the calculated PMGF frequencies are determined for different distances, without confidence intervals. The model
predicted PMGF frequencies (0.46, 0.32, 0.22 and 0.12 %)
at the distance intervals of 0.3, 1.2, 2.4 and 6 m based on
the calculating tool are similar to those (0.30–0.97, 0.05–
0.33, 0.02–0.22 and 0.02–0.07 %) obtained from the
PMGF experiments at the corresponding distance intervals (see Table 3 in Bae et al. 2013).
PMGE frequencies of wheat. For the wheat crop-to-crop
gene flow case study, we calculated PMGF frequencies of
this crop based on the following five parameters obtained from published results: pollen diameter to be
50 lm, pollen release height to be 0.5 m, outcrossing
rate to be 0.5 %, crossability to be 90 % and wind speed
to be 4.5 m s 1 (Beckie et al. 2011; Wang et al. 2016).
A PMGF frequency (F ¼ 0.086 %) for the target wheat
recipient at a given spatial distance interval (e.g. 5 m)
was calculated and displayed by the tool (Fig. 4A, at the
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Figure 3. Gene flow in rice case study. (A) The display of a PMGF
(PMGF) frequency (F ¼ 0.46 %) at 0.3 m; (B) the display of PMGF frequencies at different spatial distances (0.3–80 m); (C) the display
of gridlines.
lower side) after including the five parameters (Fig. 4A)
and distance to recipient (e.g. 5 m) of wheat and clicking
the ‘Gene flow frequency (F)’ button. A series of calculated PMGF frequencies (0.086–0.013 %) for a given
spatial-distance range (5–80 m) was shown as a curve in
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Figure 4. Gene flow in wheat case study. (A) The display of a PMGF
frequency (F ¼ 0.086 %) at 5 m; (B) the display of PMGF frequencies
at different spatial distances (5–80 m); (C) the display of gridlines.
Figure 5. Gene flow in maize case study. (A) The display of a PMGF
frequency (F ¼ 19.50 %) at 2 m; (B) the display of PMGF frequencies
at different spatial distances (2–80 m); (C) the display of gridlines.
the plotting field (Fig. 4B, at the right) when clicking the
‘Frequency decline by distance’ button. Gridlines will be
shown in the plot field (Fig. 4C) by clicking the ‘Gridlines’
button. The model predicted PMGF frequencies (0.086,
0.058, 0.038 and 0.029 %) at the distance intervals of 5,
10, 20 and 30 m based on the calculating tool are similar
to those (0.07–0.09, 0.05–0.07, 0.03–0.04 and 0.01–
0.02 %) from the field experiments at the corresponding
distance intervals (see Fig. 5 in Beckie et al. 2011).
PMGE frequencies of maize. Using maize crop-to-crop
gene flow as an example, we calculated PMGF frequencies of this crop by the five parameters as follows: pollen
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diameter to be 100 lm, pollen release height as 1.5 m,
outcrossing rate to be 50 %, crossability to be 90 % and
wind speed to be 5 m s 1 (Weekes et al. 2007; Wang
et al. 2016).
After including the five parameters (Fig. 5A) and distance to recipient (e.g. 2 m) for maize, and clicking the
‘Gene flow frequency (F)’ button, a calculated PMGF frequency (F ¼ 19.5 %) for the target maize recipient at a
given spatial distance interval (2 m) was displayed (Fig.
5A, lower side). When clicking the ‘Frequency decline by
distance’ button, a series of calculated PMGF frequencies
(19.5–0.70 %, as a curve) at a range of distance intervals
(2–80 m) was displayed in the plotting field (Fig. 5B, at
the right). Gridlines will be displayed in the plot field (Fig.
5C), when clicking the ‘Gridlines’ button. The model predicted PMGF frequencies (19.5, 13.2, 8.7 and 3.5 %) at
the distance intervals of 2, 5, 10 and 30 m based on the
calculating tool are similar to those (21–22, 12–13, 7–8
and 4–5 %) obtained from the field experiments at the
corresponding distance intervals (see Fig. 2 in Weekes
et al. 2007).
Altogether, these results from the rice, wheat and
maize gene flow case studies indicated that the calculating tool can generate relatively reliable PMGF frequencies
for plant species.
Discussion
We constructed a tool to calculate the frequency of
PMGF based on the quasi-mechanistic PMGF model
(Wang et al. 2016) that was selected among a large
number of published PMGF models. The selection of the
quasi-mechanistic model of Wang et al. (2016) to construct the PMGF calculating tool is due to the reason that
this model can provide PMGF predictions with a relatively
high level of accuracy by the inclusion of both biological
and climatic parameters. Furthermore, the model-based
PMGF calculating tool has an easy-operating interface
due to the practical design of a human–computer dialog
system, which can be easily handled by any users who
do not have sufficient knowledge on mathematical modelling. To our knowledge, this is the first available calculating tool that can be used to estimate PMGF
frequencies of a pollen-donor species/variety to its pollen
recipients at a given spatial distance(s) based on a PMGF
mathematical model. The advantage of such a calculating tool is its simplified procedure of model-based prediction for PMGF frequencies, which makes the
complicated theoretical PMGF modelling applicable. This
applied feature has not been achieved by the other available PMGF modelling studies that only provide mathematical equations (e.g. Klein et al. 2006; Wang and Yang
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2010; Hu et al. 2014). Other types of published PMGF
models may also be transformed into practical tools for
calculating PMGF frequencies. Yet, it is necessary to fully
understand the underlying mechanisms of the models.
The calculating tool includes four biological parameters: pollen diameter, pollen release height, outcrossing
rate and crossability, in addition to a climatic parameter.
These biological parameters can be measured directly
from the target plant species/varieties at the field sites
where PMGF frequencies need to be obtained. The
required climatic parameter (wind speed) can also be
measured simultaneously at the sites during the period
when PMGF frequency estimation is required. That is to
say, the prediction of PMGF frequencies can be relatively
easily achieved at any target field sites or in the particular environment, provided that the required parameters
are available through field or laboratory experiments. It
is not necessary to generate parameters by conducting a
specific PMGF experiment. Therefore, the calculating tool
from this study can facilitate the prediction of PMGF frequencies with faster and more effective characteristics,
although it is only suitable for wind-pollination plants.
To examine the predicting power of the calculating
tool, we compared the crop-to-crop PMGF frequencies
generated from this model-based tool and those obtained from published PMGF experiments, using rice,
wheat and maize as case studies (Weekes et al. 2007;
Beckie et al. 2011; Bae et al. 2013). We found that the
predicted PMGF frequencies are similar to those from
field experiments. The results indicate that the calculating tool has a relatively strong predicting power for estimating PMGF frequencies of different plant species under
various environmental conditions where the required
parameters are obtained. Apparently, this calculating
tool is designed to estimate PMGF frequencies from a
donor field to a recipient field in pure stands, which may
not be suitable for donor and recipient plants that are
grown in mixture, such as different types of trees in forests. In addition, it is also necessary to point out that this
tool does not include parameters such as air temperature and relative humidity that may also affect PMGF as
suggested by Rong et al. (2010). This is due to our limited
understanding of the contribution of these parameters
to PMGF. Future studies should be carried out to generate
knowledge on the intimate relationship of parameters,
such as air temperature and relative humidity, with
PMGF for designing an improved PMGF calculating tool
with increased accuracy.
This calculating tool has relatively wide applications
associated with PMGF. The most pertinent use of this tool
is to estimate transgene flow frequencies from GE crops
to their non-GE counterparts and to wild/weedy relative
species, which is important to assess social-economic
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and particularly environmental impacts caused by transgene flow as discussed previously (Ellstrand 1992, 2003;
Yong and Kim 2001; Lu and Snow 2005; Loureiro et al.
2009; Lu and Yang 2009). If a transgene can move from
a GE crop to its wild/weedy relatives at a comparatively
high frequency (Song et al. 2003a; Chen et al. 2004;
Weekes et al. 2005) and bring considerable fitness effects (benefit or cost) to the wild or weedy relatives
(Yang et al. 2011; Li et al. 2016), rigorous biosafety measures should be taken to minimize the undesired environmental consequences (Lu and Snow 2005; Lu and Yang
2009; Lu et al. 2016).
In a coexistence agro-ecosystem, the determination
of spatial isolation distances between GE and non-GE
crops is critical to reduce transgene flow frequencies to a
legally permitted threshold for non-GE crops (Devos et al.
2009). Currently, the spatial isolation distance is determined essentially based on PMGF experiments (Rong
et al. 2007; Sanvido et al. 2008; Langhof et al. 2010). The
PMGF experiments require a great amount of financial
and labor inputs. The calculating tool established in this
study can facilitate the determination of spatial isolation
distances between the coexisting GE and non-GE crops
based on the required threshold PMGF frequencies. For
example, the isolation distances between GE and non-GE
maize were determined as 50 m for an allowed threshold
of LLP of transgenes (0.9 %) based on PMGF experiments
(Sanvido et al. 2008; Langhof et al. 2010). Similarly, the
PMGF frequency calculated using our tool is 0.86 % for
maize at the isolation distance of 50 m (under a normal
wind speed of 3 m s 1), which is about the same as that
proposed by Sanvido et al. (2008) and Langhof et al.
(2010). This indicates that our PMGF calculating tool can
be used in determining the isolation distance for the coexisting GE and non-GE crops.
In addition, our PMGF calculating tool can also be
applied to determine the isolation distances for the
production of certified seeds between field plots to
guarantee the purity of the bred seeds used for agricultural production. For example, according to the criteria of different countries for certified seed
production, the proposed allowance (threshold) for
the mixture of undesired seeds for rice is 0.23 % and
for maize is 0.50 % (see Table 2 in Zhang et al. 2011).
On the other hand, Yong and Kim (2001) suggested
the minimum spatial isolation distance to reach the
allowed mixture of undesired seeds for different crops,
which is 3 m for rice and 200 m for maize. To examine
whether the proposed isolation distances (3 and 200
m) meet the criteria of allowed mixture (%) for rice
and maize in seed production, we used this tool to calculate the frequencies of PMGF from undesired sources of crops. Consequently, the calculated frequency
AoB PLANTS www.aobplants.oxfordjournals.org
is 0.23 % for rice at the isolation distance of 3 m and
0.21 % for maize at the isolation distance of 200 m
under a wind speed of 5 m s 1, which are within the
threshold of seed mixture for rice and maize seed production, respectively. This demonstrates that our
PMGF calculating tool can be applied to determine the
isolation distances of certified seed production for different crop species, provided that the parameters are
obtained at the field sites where the certified seeds
are produced. In addition, the prediction of PMGF frequencies using the PMGF calculating tool may also be
useful for the studies of evolutionary and conservation
biology of wild plant species. As an evolutionary driving force, gene flow plays an important role in influencing evolution of plant species, particularly for
endangered wild species (Ellstrand et al. 2013;
Ellstrand 2014). For example, the extensive gene flow
mediated by pollination from cultivated rice to wild
rice (Oryza rufipogon) that contains valuable genetic
diversity for rice breeding may result in considerable
losses of genetic integrity or even local extinction of
this species (Song et al. 2003b). If PMGF frequencies at
given spatial distances can be determined using a calculating tool, proper measures can be taken in advance to avoid such losses of genetic diversity for
many wild-relative species.
Conclusions
Based on the published quasi-mechanistic PMGF model
(Wang et al. 2016), we constructed a tool/software that
can accurately calculate PMGF frequencies of windpollination plant species by the inclusion of four biological and one climatic (wind speed) parameters. This tool
can be easily applied by any users who are not familiar
with mathematical modelling, provided that the required
biological and climatic parameters are available. These
parameters can be measured either directly at the target
field sites/laboratories or obtained from relevant published data, without conducting a specific PMGF experiment, which makes the estimate of PMGF frequencies
relatively easy and practical under different environmental conditions. Comparison between the calculated PMGF
frequencies using this tool and those from published
PMGF experimental data showed a good accordance between the two sets of data, suggesting the high prediction power of this tool. Therefore, this PMGF calculating
tool with its easy-operating, practical and accurate features will be greatly useful for estimating transgene flow
frequencies that are associated with potential socialeconomic and environmental biosafety impacts. This
tool can also be used to determine the spatial isolation
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distances between GE and non-GE crops within particular
threshold frequencies for GE crop presence (LLP) in the
coexistence farming systems (Devos et al. 2009; Lu and
Yang 2009). In addition, this tool can also be used to facilitate the determination of proper spatial isolation distances between field plots for producing certified crop
seeds to guarantee the seed purity by maintaining the
mixture of undesired seeds from PMGF within the
allowed threshold (Zhang et al. 2011).
Sources of Funding
This work is supported by the Natural Science
Foundation of China (31330014) and the National
Program of Development of Transgenic New Species of
China (2016ZX08011-006).
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Contributions by the Authors
L.W. established and tested the calculating tool, and
wrote the manuscript. B.-R.L. designed the study and
wrote the manuscript.
Conflict of Interest Statement
None declared.
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